# How to find current density given resistor, and voltage, using Ohm's law in this case?

I was wondering about how to find current density, given a resistor and an electromotive force.

resistor's data are: resistivity = $$\rho$$, length = $$l$$, and cross sectional area = $$A$$. resistor = $$\rho * \frac{l}{A}$$. electromotive force is equal to Ohm's law, $$EMF = R*I$$, but I need to use microscopic version of Ohm's law, because I need to find current density. $$E = \rho * j$$, and therefore current density is equal to $$j = \frac{E}{\rho}$$, I have a question:

is $$E$$ equal to $$EMF$$? why? why not?

if they are the same thing, then I can use microscopic version of Ohm's law, I know $$EMF = E$$, and I know $$EMF$$. Otherwise I don't know what to do in order to find $$E$$.

• Electromotive force comes from a battery or a voltage source. If you connect your resistor to the battery it will be responsible for a current flow an $V_{bat} = I \cdot R = E \cdot l$ Jul 10, 2022 at 9:47
• $E = \frac{I*R}{l} = V_(bat)$, right? okay, it was just algebra Jul 10, 2022 at 9:56
• not right V=IR not IR/L Jul 10, 2022 at 9:59
• EMF and electric potential (Voltage, V) have the same effect on charges, so they are generally numerically equal. Jul 10, 2022 at 11:21
• in your definition $E l = V$ Jul 11, 2022 at 11:42

For current density just use I/A or E=U/L

• what does U stand for? Jul 10, 2022 at 10:09
• @GabrielBurzacchini U is European for potential difference. Jul 10, 2022 at 14:58